Cyber digital twin simulator for security controls requirements

ABSTRACT

Implementations include receiving an AAG that at least partially defines a digital twin of an enterprise network and includes rule nodes each representing an attack tactic that can be used to move along a path, determining security controls each mitigating at least one rule node, executing an iteration of a simulation of a sub-set of security controls in the enterprise network, the iteration including: for each security control in the set of security controls, determining, an influence score that represents a change in a security risk from implementing the security control and a rule distribution, defining the sub-set of security controls based on the first influence scores, and reducing the AAG based on the sub-set of security controls to provide a residual AAG, determining a decrease in a graph risk value and the first AAG, and selectively implementing the sub-set of security controls in the enterprise network.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Application No. 62/983,040, filed on Feb. 28, 2020, the disclosure of which is expressly incorporated herein by reference in the entirety.

BACKGROUND

Computer networks are susceptible to attack by malicious users (e.g., hackers). For example, hackers can infiltrate computer networks in an effort to obtain sensitive information (e.g., user credentials, payment information, address information, social security numbers) and/or to take over control of one or more systems. Computer networks are used to execute processes that support operations of enterprises and/or industrial infrastructures. Enterprises, in general, and industrial infrastructures, in particular, are increasingly connected to external networks such as the Internet. As such, processes that were once isolated from the open Internet network, are now vulnerable to external cyber-attacks. As the frequency and derived impact of these attacks increase, there is a need to prioritize and mitigate risks in order of importance to the operations.

To defend against such attacks, enterprises use security systems to monitor occurrences of potentially adverse events occurring within a network, and alert security personnel to such occurrences. For example, one or more dashboards can be provided, which provide lists of alerts that are to be addressed by the security personnel. However, the scale and complexity of cyber threats in digital enterprises hamper operator ability to gather, prioritize, and rationalize which security controls requirements should be handled first for achieving rapid risk reduction.

SUMMARY

Implementations of the present disclosure are directed to mitigating cyber security risk in enterprise networks. More particularly, implementations of the present disclosure are directed to a Cyber Digital Twin (CDT) platform that executes simulations on a digital twin of an enterprise network to determine and prioritize security controls requirements to mitigate cyber security risk in the enterprise network.

In some implementations, actions include receiving an analytical attack graph (AAG) representing paths within the enterprise network with respect to at least one target asset, the AAG at least partially defining a digital twin of the enterprise network and includes a set of rule nodes, each rule node representing an attack tactic that can be used to move along a path, determining a set of security controls, each security control mitigating at least one rule node in at least a sub-set of rule nodes of the set of rule nodes, executing a first iteration of a simulation representing implementation of a first sub-set of security controls in the enterprise network, the first iteration including: for each security control in the set of security controls, determining, a first influence score that represents a change in a security risk that would result from implementing the security control and a rule distribution representing one or more rules that the security control mitigates, defining the first sub-set of security controls based on the first influence scores, and reducing the AAG based on the first sub-set of security controls and a first reduction method to provide a first residual AAG, determining a decrease in a graph risk value based on the AAG and the first residual AAG, and selectively implementing the first sub-set of security controls in the enterprise network at least partially in response to the decrease in the graph risk value. Other implementations of this aspect include corresponding systems, apparatus, and computer programs, configured to perform the actions of the methods, encoded on computer storage devices.

These and other implementations can each optionally include one or more of the following features: the first reduction method includes one of a gradient reduction, an area under curve (AUC) reduction, a top k reduction, and a custom reduction; actions further include executing a second iteration of the simulation representing implementation of a second sub-set of security controls in the enterprise network, the second iteration including, for each security control in a residual set of security controls, determining, a second influence score that represents a change in a security risk that would result from implementing the security control and a rule distribution representing one or more rules that the security control mitigates, defining the second sub-set of security controls based on the second influence scores, and reducing the AAG based on the second sub-set of security controls and a second reduction method to provide a second residual AAG; the second reduction method includes one of a gradient reduction, an AUC reduction, a top k reduction, and a custom reduction; determining a decrease in a graph risk value is further based on the second residual AAG; the residual set of security controls is provided based on a residual set of rule nodes of the first residual AAG; determining a set of security controls at least partially includes cross-referencing each rule represented in the AAG with a traceability matrix that maps security controls to rules; and the first reduction method is automatically selected based on a curve representative of an influence score histogram for the set of security controls.

The present disclosure also provides a computer-readable storage medium coupled to one or more processors and having instructions stored thereon which, when executed by the one or more processors, cause the one or more processors to perform operations in accordance with implementations of the methods provided herein.

The present disclosure further provides a system for implementing the methods provided herein. The system includes one or more processors, and a computer-readable storage medium coupled to the one or more processors having instructions stored thereon which, when executed by the one or more processors, cause the one or more processors to perform operations in accordance with implementations of the methods provided herein.

It is appreciated that methods in accordance with the present disclosure can include any combination of the aspects and features described herein. That is, methods in accordance with the present disclosure are not limited to the combinations of aspects and features specifically described herein, but also include any combination of the aspects and features provided.

The details of one or more implementations of the present disclosure are set forth in the accompanying drawings and the description below. Other features and advantages of the present disclosure will be apparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an example architecture that can be used to execute implementations of the present disclosure.

FIG. 2 is an example influence score histogram that illustrates contribution of security controls to an overall cyber risk exposure of an enterprise.

FIG. 3 is an example security controls histogram that illustrates risk reduction simulation using a security controls technique.

FIG. 4 is an example security controls curve that illustrates risk reduction simulation using a gradient reduction technique.

FIG. 5 is an example security controls curve that illustrates a risk reduction simulation using an area under the curve technique.

FIG. 6 depicts an example agile Security (AgiSec) system architecture with the addition of an Agile Security Controls (AgiSC) module.

FIG. 7 depicts an example user interface in accordance with implementations of the present disclosure.

FIG. 8 is a flowchart of an example process that can be executed in accordance with implementations of the present disclosure.

FIGS. 9A-9C depicts an evolution of an example AAG over multiple iterations in accordance with implementations of the present disclosure.

FIGS. 10A-10C depicts an evolution of an influence histogram corresponding to the example AAG of FIGS. 9A-9C.

FIG. 11 depicts a graph depicting an example graph risk value decay over iterations in accordance with implementations of the present disclosure.

Like reference numbers and designations in the various drawings indicate like elements.

DETAILED DESCRIPTION

Implementations of the present disclosure are directed to mitigating cyber security risk in enterprise networks. More particularly, implementations of the present disclosure are directed to a Cyber Digital Twin (CDT) platform that executes simulations on a digital twin of an enterprise network to determine and prioritize security controls requirements to mitigate cyber security risk in the enterprise network.

In some implementations, actions include receiving an analytical attack graph (AAG) representing paths within the enterprise network with respect to at least one target asset, the AAG at least partially defining a digital twin of the enterprise network and includes a set of rule nodes, each rule node representing an attack tactic that can be used to move along a path, determining a set of security controls, each security control mitigating at least one rule node in at least a sub-set of rule nodes of the set of rule nodes, executing a first iteration of a simulation representing implementation of a first sub-set of security controls in the enterprise network, the first iteration including: for each security control in the set of security controls, determining, a first influence score that represents a change in a security risk that would result from implementing the security control and a rule distribution representing one or more rules that the security control mitigates, defining the first sub-set of security controls based on the first influence scores, and reducing the AAG based on the first sub-set of security controls and a first reduction method to provide a first residual AAG, determining a decrease in a graph risk value based on the AAG and the first residual AAG, and selectively implementing the first sub-set of security controls in the enterprise network at least partially in response to the decrease in the graph risk value.

As described in further detail herein, implementations of the present disclosure provide a CDT platform that executes simulations using a digital twin of an enterprise network based on attack graph analytics. In some implementations, the cyber digital twin, also referred to herein as digital twin, is used to automatically gather and prioritize security requirements at scale over a respective (active) enterprise network. The digital twin represents information about the computer network, and is used to associate the information with attack tactics, measure the efficiency of implemented security controls requirements, and automatically detect missing security controls. The digital twin is used to evaluate cyber risk, measured as a risk value, over the attack graphs and proposes prioritization of detected requirements towards rapid reduction of risk under active system constraints. In some implementations, a CDT simulator offers several risk reduction methods for automatically selecting security controls requirements. Data used for constructing a contextual digital twin is defined including relations between security controls and attack tactics. Calculations used for ranking security controls risk impact, the algorithm for security controls requirements prioritization, and a demonstration of successful results using a field experiment conducted on an active enterprise network are each described in further detail herein.

FIG. 1 depicts an example architecture 100 in accordance with implementations of the present disclosure. In the depicted example, the example architecture 100 includes a client device 102, a network 106, and a server system 108. The server system 108 includes one or more server devices and databases (e.g., processors, memory). In the depicted example, a user 112 interacts with the client device 102.

In some examples, the client device 102 can communicate with the server system 108 over the network 106. In some examples, the client device 102 includes any appropriate type of computing device such as a desktop computer, a laptop computer, a handheld computer, a tablet computer, a personal digital assistant (PDA), a cellular telephone, a network appliance, a camera, a smart phone, an enhanced general packet radio service (EGPRS) mobile phone, a media player, a navigation device, an email device, a game console, or an appropriate combination of any two or more of these devices or other data processing devices. In some implementations, the network 106 can include a large computer network, such as a local area network (LAN), a wide area network (WAN), the Internet, a cellular network, a telephone network (e.g., PSTN) or an appropriate combination thereof connecting any number of communication devices, mobile computing devices, fixed computing devices and server systems.

In some implementations, the server system 108 includes at least one server and at least one data store. In the example of FIG. 1, the server system 108 is intended to represent various forms of servers including, but not limited to a web server, an application server, a proxy server, a network server, and/or a server pool. In general, server systems accept requests for application services and provides such services to any number of client devices (e.g., the client device 102 over the network 106). In accordance with implementations of the present disclosure, and as noted above, the server system 108 can host a CDT platform.

In the example of FIG. 1, an enterprise network 120 is depicted. The enterprise network 120 represents a network implemented by an enterprise to perform its operations. In some examples, the enterprise network 120 represents on-premise systems (e.g., local and/or distributed), cloud-based systems, and/or combinations thereof. In some examples, the enterprise network 120 includes IT systems and OT systems. In general, IT systems include hardware (e.g., computing devices, servers, computers, mobile devices) and software used to store, retrieve, transmit, and/or manipulate data within the enterprise network 120. In general, OT systems include hardware and software used to monitor and detect or cause changes in processes within the enterprise network 120 as well as store, retrieve, transmit, and/or manipulate data. In some examples, the enterprise network 120 includes multiple assets. Example assets include, without limitation, users 122, computing devices 124, electronic documents 126, and servers 128.

In some implementations, the CDT platform is hosted within the server system 108, and monitors and acts on the enterprise network 120, as described herein. More particularly, and as described in further detail herein, the CDT platform executes simulations on a digital twin of an enterprise network (e.g., the enterprise network 120) to determine and prioritize security controls requirements to mitigate cyber security risk in the enterprise network. In some examples, the CDT platform is provided as part of a security platform, such as an agile security platform discussed herein. In some examples, the CDT platform is separate from and interacts with a security platform, such as the agile security platform discussed herein. As described in further detail herein, one or more security controls can be implemented in the enterprise network 120 based on security controls requirements identified through simulation in order to reduce risk of cyber-attack in the enterprise network 120.

To provide further context for implementations of the present disclosure, in the area of cyber security resiliency (e.g., how resilient an enterprise network is to cyber-attack), enterprise practitioners may rely on the implementation of procedures, processes, and automation tools, which can be collectively referred to as Security Controls (SCs). In general, a SC (also referred to as a remediation action) can be associated with a fact and/or a rule, as a known remediation action for mitigating the fact and/or rule (e.g., preventing the fact from occurring by preventing execution of a rule). An example SC can include, without limitation, installing a security patch to resolve a vulnerability of a particular version of software. Executing efficient SCs is aimed at preventing and handling security issues and problems prior to the materialization of the consequent cyber risk. Such security issues are introduced to the enterprise cyber space in an overwhelming rate, driving the need for constant optimization and prioritization of requirements that are more critical to the business first, followed by automatic implementation to remediate the imminent cyber risks. In addition, being able to trace the enterprise cyber posture to employed automation and practices of SC requirements (SCRs) is not a direct indication of success in preventing attacks by hackers. As such, goals of employing SCs are to reduce the attack surface over time as suggested by compliance drives, and focus less on prevention of coordinated attacks and imminent risk reduction toward targeted crown jewels.

Investment in SCs materializes in tools and processes aimed at solving optimized and automated known security needs, while other investments in SCs are projected and planned according to new types of threats, or adjustments to new and more efficient security tools. The existing implementation of SCs may be evaluated by constantly tracing and correlating security requirements with the active attack surface of the network, such as discovering and analyzing pathways to specific targets. As the attack surface mutates due to new threat intelligence introduced and changes in the infrastructure settings and configuration, implemented security tools can become invalid, while new tools may be inadequate.

One option to evaluate the efficiency of implemented security tools or detecting a gap that highlights missing SCs is by understanding how hackers may move within the network. Exploitation of vulnerabilities in the network is done by performing lateral movements between acquired IT assets. Such actions are possible due to missing implementation of some SCs that could have prevented these actions in the first place. As such, the pure existence of modeled attack pathways is an indication of lack of performance or missing implementation of SCRs. Compliance needs and standards are key drivers for defining security requirements that are manifested in SCs. Such needs are adjusted to the type of the organization domain, the type of network, connected systems, etc. As discussed herein, such definitions of requirements do not consider potential movements of hackers in the network, exploiting existing vulnerabilities within the context of targeted attack pathways. The context of the network hackability state is missing from the considerations and definitions of the requirements.

A connection between the ability to hack an active system and automatically discover SCRs in a context of potential cyber-attacks is described herein. A method and technology for constructing a contextual cyber digital twin that maps the relations between SCs and attack tactics that, in turn, represent SCRs are also described in detail herein. Also described are definitions of SCs and types of attack graphs, and a framework and method for using a cyber digital twin that captures attack pathways as a means for discovering SCRs. The methodology details how to measure an impact of an attack and the relation to relevant SCs as well as ways for prioritization of SCRs to reduce the risk impact as quick as possible. A simulator is provided for performing the SCRs analysis, including incremental and iterative manner for rapid decay of risk. In some examples, SCs refer to a set of SCs (e.g., one or more SCs), each SC being a tool (e.g., software) and/or action that can be executed in the enterprise network to mitigate risk. In some examples, SCRs refer to a set of SCRs (e.g., one or more SCRs), each SCR representing an absence of a SC in the enterprise network that should be addressed by implementing a SC to mitigate risk.

In some examples, SCs may be defined as a combination of policies, methods, and tools that are aimed at protecting an enterprise network from cyber-attack. In some examples, SCs are classified into fourteen groups according to ISO/IEC 27001 standards, while the U.S. government's National Institute of Standards and Technology (NIST) provides seventeen groups of SCs. To illustrate the implications of SCs in the present disclosure, some of the classifications listed in Table 1 are used.

TABLE 1 Example SC Groups by Industry Standarization Authorities. ISO/IEC 27001 NIST, 800-53, Revision 4 A.5: Information security policies AC: Access Control A.6: How information security is AT: Awareness and Training organized AU: Audit and Accountability A.7: Human resources security CA: Security Assessment and A.8: Asset management Authorization A.9: Access controls and managing CM: Configuration Management user access CP: Contingency Planning A.10: Cryptographic technology IA: Identification and A.11: Physical security and Authentication equipment IR: Incident Response A.12: Operational security MA: Maintenance A.13: Secure communications and MP: Media Protection data transfer PE: Physical and Environmental A.14: Secure acquisition, Protection development, and support PL. Planning of information systems PS: Personnel Security A.15: Security for suppliers and RA: Risk Assessment third parties SA: System and Services A.16: Incident management Acquisition A.17: Business continuity and SC: System and Communications disaster recovery Protection A.18: Security Compliance SI: System and Information Integrity

Each SC group depicted within Table 1 contains specific policies. Examples are the ISO/IEC 27001 A.8 asset management group, that contains policy #8.1.1 for asset inventory and policy #8.1.3 for assets acceptable usage, for example. Described in further detail herein is a mechanism and technology for detecting and tracking missing implementations of specific sub-set of security requirements that are part of the generic SCs, yet specifically relevant to the context of an enterprise network that is under analysis. Consequently, the technology supports the evaluation of SCs effectiveness and allocated capital relevant to the enterprise network under investigation and tuned to defined business targets.

SCRs can be gathered in various manners. In some implementations, a detailed analysis of assets of an enterprise network is performed and an implementation plan based on best practices is provided. In some implementations, SCRs can be generated from an examined system using industry standards. Some implementations for cyber security investment assessment rely on methods of game theory, multi-objective optimization, stochastic calculus, and other ideas. For example, the investment strategy may be modeled as a game between a defender and an attacker. The defender's goal may be to assemble a defense toolkit that would minimize potential attack damage given a limited budget constraint. The task may be reduced to an optimization problem and solved by algorithms such as the Knapsack problem. The underlying data used is the output of a network scanner as well as information about vulnerabilities published at a public catalog such as the National Vulnerability Database (NVD) provided by the U.S. government. However, despite the validity and efficiency of this mathematical apparatus, the approach may not address how the vulnerabilities are exploited in practice during a real-life, targeted attack. If an attack is undertaken against a specific target or a set of targets within a computer network, a different location of identical vulnerabilities in the network has a different impact. Possible attacker actions and different pathways to the targets that generate different impacts may be included in evaluation of security control effectiveness.

Attack pathways can be modeled as attack trees, petri nets, and lately mostly used, as attack graphs. Modeling approaches that capture nodes as physical assets (e.g., a workstation machine) and edges as potentials lateral movements of a hacker between two assets are referred to as Physical Attack Graphs (PAG). Modeling logical rules that define how an attacker advances within the network are represented in Analytical Attack Graphs (AAGs). These logical rules are in essence a representation of security requirements, as enablers to adversarial lateral movement, which a defender is required to eliminate and nullify. Use of AAGs in mitigating attacks on computer networks is described in further detail in commonly assigned U.S. application Ser. No. 16/554,846, entitled Generating Attack Graphs in Agile Security Platforms, and filed on Aug. 29, 2019, the disclosure of which is expressly incorporated herein by reference in the entirety for all purposes. Further, generation of AAGs is described in further detail in commonly assigned U.S. application Ser. No. 16/924,483, entitled Resource-efficient Generation of Analytical Attack Graphs, and filed on Jul. 9, 2020, the disclosure of which is expressly incorporated herein by reference in the entirety for all purposes.

In some implementations, cyber security investment analysis relies on attack graphs. In some implementations, the problem of SCRs is modeled as a multi-objective optimization problem with the goals of: (1) minimizing the cyber security risk on targets, (2) reducing direct costs of a security control deployment, and (3) reducing indirect costs of security control implementation. An example of indirect cost is employee's loss of time due to more sophisticated compliance procedures.

In some implementations, attack graphs may be generated based on network scanners output, known published vulnerabilities, and network related data sources (e.g., firewall rule analyzers) as a good approximation to some types of attacks. Probabilistic graphical models, such as Bayesian networks, can be used to reflect difficulty differences of exploiting vulnerability. However, modern attacks are more sophisticated. To model a hacker's movement adequately during a complex attack, not only endpoint vulnerabilities and network firewall rules should be considered, but also amongst other, user access permissions and open sessions status. In some implementations, a complete approach to address the complexity of a modern attack may be used. AAGs may be created based on a wide range of facts about the network assets and their interaction. The data can be received from multiple sources and can include features such as, for example, user account hierarchies, complete software installation compared to those detected by port scanner, clear access authorization credentials, and others. In some examples, rules may be provided from the MITRE ATT&CK™ knowledgebase of attack tactics.

In accordance with implementations of the present disclosure, the CDT platform generates detailed AAGs to multiple targets with multiple origins. A digital twin can be described as a software-implemented replica of a physical entity that captures aspects of the physical entity. In the instant case, the physical entity is an enterprise network and an aspect is a cyber security posture. A digital twin is unique, because it captures and models the aspect of the enterprise's cyber security posture from a hacker's perspective and models hacker's movements, instead of the pure system monitored state. In short, the digital twin can be described as an inferencing model of the enterprise network.

As described in further detail herein, the CDT platform of the present disclosure enables creation and use of digital twins for automatically gathering and prioritizing SCRs within large industrial settings, where scale and complexity hampers the ability of manual analysis. More particularly, the CDT platform includes a simulator that tracks lack of SCRs implementation within the context of targets that are exposed to cyber security risks. The analysis of the attack graph towards which set of SCRs should be implemented first, is aimed at rapidly reducing the attack surface size. As such, the simulation examines how the implementation of a set of SCs can affect the organization's overall cyber risk exposure. Described in further detail herein are details of the methodology and the data types the simulator uses, the attack graph in the form of AAG, a SCs Traceability Matrix™ and a set of configuration parameters. For illustrative purposes, the SCs are selected to be policies and rules extracted from the ISO/IEC 27001 standard. In some cases, a goal of an enterprise is to comply with these policies. In other cases, the goal may be to prioritize budget proposals or to assess effectiveness of previous year budget allocations for cyber security tools. In real world scenarios, the SCs could be mapped to projects that represent cyber security budget proposals.

An attack graph is based on associating rules and impacts according to facts (each of rules, impacts, and facts being represented as respective nodes) that are based on evidence collected from Configuration Items (CI). CIs are network assets such as computers, user accounts, and the like. Some of the CIs can be target CIs, commonly referred to as crown jewels, which are highly valuable machines, applications, or processes. Rules are attack tactics that are derived from the collected facts, forming associations and links in the graph. Rules can be provided from a data source, such as the rules provided from MITRE ATT&CK™. Facts can be information on the CI such as, for example, identification, configuration, installed software and its version, open sessions, memory map, vulnerability, user group membership, or a network share access permission, and the like. Rules represent needed SCRs to be implemented. SCRs can be, for example, to isolate an application in a sandbox, to disable a program, segment a network, to change user privileges, and the like. Consequently, a rule may be to implement one of the former requirements in order to prevent the ability to and attack tactic of executing a code on a remote machine, for example. Impacts are the outcomes of not implementing a rule inference (e.g., ability to elevate user privileges on a given machine under a specific account). The discovered information is fed into a proprietary rule engine that uses the discovered facts, applies the rules, and generates the impacts, in an aggregated manner across all CIs, towards all target CIs (crownjewels). The output of the process is the attack graph (e.g., AAG).

In order to evaluate the success of risk reduction and to decide which SCRs to prioritize, a Graph Risk Value (GRV) is defined, as in Eq. 1, as a measure of the cyber risk exposure of the enterprise network. GRV is a single-valued scalar metric that is related to an exponential cost model and can be provided as:

GRV=Σ_(i∈M) R _(i)  (1)

where R_(i) is a risk measure of an individual target impact and M is a set of target impacts. Risk can be determined as follows:

$\begin{matrix} {R_{i} = {e^{- \frac{Ht}{\alpha}} \cdot C_{i}}} & (2) \end{matrix}$

where H_(i) is hardness of all paths to target i, α is damping constant (e.g., α=8), and C_(i) is a graph theory eigenvector centrality measure of target impact node in the modeled AAG. Hardness is a value defined by a cyber security expert for each rule indicating how difficult the rule is to perform based on, for example, available tools, script, previous experience and the like. In some examples, H_(i) is calculated as an average over all rules on all paths that lead to a target. The rules that are used to generate the AAG may be defined by cyber security experts. For each rule, the experts may also define a set of SCs that can mitigate the effect of the rule.

To illustrate this principle, an example attack tactic is referenced. The example attack tactic includes T1175 (provided from MITRE ATT&CK™) that defines a lateral movement of a hacker from one machine to another, by utilizing MS Windows DCOM infrastructure. In order to use this tactic, an adversary must acquire a user account with certain privileges. Such an account should be a member of the Distributed COM group on a host machine. Consequently, the hacker can perform a remote procedure call (RPC) over the network to a target machine. In addition, the target machine must be listening on a predefined set of ports supported by DCOM infrastructure. To mitigate the exposure to this type of attack, MITRE offers several tactics that are mapped to SCs defined by ISO/IEC 27001 standard as depicted in Table 2.

TABLE 2 Example of Requirements for T11175. Proposed Mitigation for T1175 Required Security Controls (MITRE ATT&K) (ISO/IEC 27001) 1. Application Isolation and Sandboxing A.9.1.1 Access Control 2. Disable or Remove Feature or Program A.9.1.2 Access to Networks 3. Network Segmentation and Network Services 4. Privileged Account Management A.13.1.3 Segregation in Networks Namely, MITRE T1175 requirements is to implement three mitigations, in which a security expert may need to implement several SCs. In the case of T1175, the security expert may opt to implement an Access Control Policy (A911), an Access to Networks and Network Services policy (A912), and a Segregation in Networks policy (A1313). By implementing even one of these three SCRs, a defender can eliminate the potential lateral movement. Accordingly, the conditional logic is an AND relation between the policies.

This Boolean condition can be defined as a Prolog rule used to generate the attack graph in the form of:

Listing 1: Example Rule in Prolog. execCode (Host, User) :=  userInLocalGroup(Host, ‘<DISTRIBUTED COM USERS>’, User) ,  canNetComm (SrcHost, Host) ,  execCode (SrcHost, User) ,  @ports Host:or (135, U135, 1029) Listing 1 is an example of a Boolean AND condition of MITRE T1175 rules (e.g., AND multiplication between existing user group, network access, and ability to remotely execute code, applied on an open port). This example Prolog syntax indicates that four conditions must be met for an adversary to be able to execute code on Host under privileges of the User account. First, userInLocalGroup indicates that a User must be a member of specified local group including indirect membership, or effective membership as a result of other attack tactics defined as rules. The second condition, canNetComm, requests a network communication between the source and destination hosts. Thirdly, the User must already be able to execute code, execCode, on the source host machine. Finally, the host must have a service listening on either one of TCP ports 135, 1029 or on UDP port 135, using the request @ports. It should be noted that the term @ports is an extension to standard Prolog syntax.

Another cardinal data set processed by the simulator is a mapping between SCs and lateral movement rules. This mapping is provided in the form of a sparse matrix that is referred to as aTraceability Matrix™. For example, TM=(tm_(ij)), where tm_(ij)≠0, if security control i can be used to mitigate attack tactic j representing a rule node in AAG, otherwise tm_(ij)=0. Possible values for tm_(ij) can include values in a set of 3 symbols: {0, *, +}.

If tm_(ij)≠0, then the relation between the SC and the attack tactic is defined by a Boolean logic operator. It may either be a logical AND (*) or a logical OR (+). A Boolean OR operator instructs implementing one SC to eliminate the risk of the attack tactic. In the example above, it is enough to either redefine user permissions or to isolate DCOM server by updating firewall rules. Each SC implementation will result in mitigation (e.g., elimination) of a particular attack-related risk. However, there could be a situation when only implementation of all SCs related to the attack tactic will lead to its elimination. In such a case, the relation is defined by a Boolean AND operator. Table 3 depicts an example TM with logical operators.

TABLE 2 SC Traceability Matrix with Logic Operators SC1 SC2 SC3 SC4 SC5 ... SCn LR1 + 0 0 + 0 ... + LR2 0 + + 0 0 ... 0 LR3 0 0 0 + + ... 0 LR4 + 0 + 0 + ... +

LRm 0 0 + 0 + ... 0 In Table 3, SC₁, SC₂, . . . SC_(N) are security controls LR₁, LR₂, . . . , LR_(M) are Lateral movement rules that are mapped to SCRs, n is index of the evaluated SC. The TM values indicate the relations between the requirements and SCs, and the exposure to a rule. The “+” symbol means a Boolean OR relations, and the “*” symbol indicates a Boolean AND.

In some implementations, the TM is used to calculate impact influence scores on each SC as provided in Eq. 3:

SC_(i)=Σ_(j∈A) tm _(ij) ·rc _(j)  (3)

where SC_(i) is influence score of security control i, rc_(j) is a count of rules that correspond to tactic j in the AAG, where function ƒ(x) is defined in Eq. 4:

$\begin{matrix} {{f(x)} = \left\{ \begin{matrix} {1,\mspace{14mu}{{{if}\mspace{14mu} x} = {{*orx} = +}}} \\ {0,\mspace{14mu}{otherwise}} \end{matrix} \right.} & (4) \end{matrix}$

The value of SC_(i) represents how many times an attacker can use the tactic within the enterprise network toward the defined target. The set A contains all implemented rules (attack tactics).

To visualize the contribution SCs make to mitigating the overall cyber risk exposure of an enterprise, an influence score histogram can be used. FIG. 2 depicts an example impact influence histogram 200. In the example of FIG. 2, the SCs are ordered by their influence score.

In some examples, different types of SCs are provided. Example types include immutable and mutable. Immutable SCs, also referred to as mandatory SCs, which cannot be eliminated due to restrictions that are not controlled by the security team, or that are not implemented at all, namely, a gap in the organization cyber resiliency. A list of immutable SCs, if there are any, is also defined as a configuration setting of the simulator.

Implementation of SCRs is costly and time consuming. The simulator conducts sensitivity analysis based on different risk reduction techniques aimed at proposing which SCs to handle first. This analysis is conducted in an iterative and incremental manner. Each technique simulates implementation of a set of SCs to consequently reduce the number of rule types in the corresponding AAG.

FIGS. 3, 4, and 5 illustrate a comparison of techniques. FIG. 3 depicts an influence score SC plotted as a histogram 300 for a small number of SCs. However, a large organization may have thousands of different SCs. FIG. 4 is a plot histogram 400 that depicts a curve that contains 3000 SCs. The histogram 400 is ordered as such that the top influencing SCs are on the left, as such an obvious strategy is to start by implementing SCs that have the highest SC influence score, and by selecting a certain quantity of those SCs. The gradient reduction technique referenced in FIG. 4 refers to an algorithm that continuously calculates the slope gradient between decaying SCs. The algorithm stops when the slope reaches a threshold value selected by the user of the simulator. This enables the user to select a point on the curve where the gradient, or the rate of change, slows down. This algorithm is useful for exponential drops. In practice this means some SCRs are disproportionate to the overall cyber security exposure of the enterprise network under investigation. An example can be to select SCs that are above 0.6 slope angle.

FIG. 4 depicts a graph illustrating the area under curve (AUC) technique. AUC is suitable for a curve with monotonic influence reduction. This is the case when there is no clear winner, and the contribution of different SCs to the overall cyber security risk is relatively uniform. The algorithm receives the percentage of AUC to reduce as a configuration parameter and enumerates the SCs which contribute to such a segment. An example can be to select the area that contains 10% of the overall number of rules in the existing AAG. The simulator provides the ability to feed a custom selection and de-selection of SCs for implementation due to business restrictions and constraints that are known to the users.

In some implementations, the CDT platform of the present disclosure can be executed as part of an agile security platform. In some examples, the agile security platform determines asset vulnerability of enterprise-wide assets including cyber-intelligence and discovery aspects of enterprise information technology (IT) systems and operational technology (OT) systems, asset value, potential for asset breach and criticality of attack paths towards target(s) including hacking analytics of enterprise IT/OT systems.

FIG. 6 depicts an example conceptual architecture 600 of an agile security (AgiSec) platform. In the example of FIG. 6, an agile security system 602 and an agile SC (AgiSC) module 604 are depicted. In some examples, the agile SC module 604 executes the simulator of the CDT platform of the present disclosure.

In further detail, the agile SC module 604 processes data provided by an agile discovery (AgiDis) module and an agile security hacker lateral movement (AgiHack) module. In some examples, the AgiDis module discovers assets and vulnerabilities of the enterprise network using third-party tools. The extracted data is stored in a data lake for further analysis by other AgiSec modules. In some examples, the AgiHack module generates an AAG of the enterpriser network by extracting AgiDis data and employing attack rules created by cyber security experts. The AgiHack module explores attack paths an attacker can traverse to advance towards targets in order to identify possible impacts on these targets. The agile SC module 604 receives the AAG from the AgiHack module and maps attack tactics of the AAG to SCs. Further detail of the agile security system 602 and the respective modules is provided in each of U.S. application Ser. No. 16/554,846 and U.S. application Ser. No. 16/924,483 introduced above. While the agile SC module 604 is depicted as being separate from the agile security system 602 in FIG. 6, it is contemplated that the agile SC module 604 can be included as part of the agile security system 602.

In some implementations, the agile SC module 604 includes a configuration defining the TM and a list of constraints over SCs, indicating which SC cannot be handled due to real-systems restrictions (e.g., mandatory SCs). In some examples, the agile SC module 604 provides output to a graphical user interface (GUI) for manual selection of a reduction technique and a decay configuration parameter per iteration. An example GUI is depicted in FIG. 7.

For each iteration, for a given input AAG, the agile SC module 604 selects SCs that are to be prioritized first, according to a selected reduction algorithm and corresponding parameters. Subsequently, the agile SC module 604 eliminates all nodes in the AAG that represent rules and requirements that are associated with the selected SCs. Pruning of the nodes results in a reduced version of the AAG, which is referred to as a residual AAG. The removed rule nodes define the current iteration list of requirements to implement, in order of importance, according to the number of appearances of the rules in the most critical SC. The agile SC module 604 creates an influence histogram that reflects the residual rules that where not handled yet. If all rules related to a certain SC were handled previously, the SC is eliminated from the remaining backlog of requirements and will no longer be presented in subsequent histograms. As the simulation progresses, each former AAG becomes an input AAG for the next iteration, and different methods of reductions can be employed. Over the iterations, the residual AAGs become sparser until the attack surface is eliminated. Subsequently, the produced list of security requirements is appended to the former batch of requirements.

FIG. 8 is a flowchart of an example process 800 that can be executed in accordance with implementations of the present disclosure. In some implementations, the example process 800 may be performed using one or more computer-executable programs executed using one or more computing devices. The example process 800 can be performed for cyber-attack risk evaluation and mitigation in accordance with implementations of the present disclosure.

Data representative of an enterprise network is received (802). For example, a discovery service (e.g., executed by the AgiDis module of FIG. 6) discovers assets and vulnerabilities of the enterprise network using third-party tools. In some examples, the discovery services scans an enterprise network to identify assets (e.g., CIs) within the enterprise network and, for each asset, information representative of a configuration of the asset (e.g., identification, configuration, installed software and its version, open sessions, memory map, user group membership, network share access permission). In some examples, vulnerabilities of one or more assets can be determined. For example, each asset can be cross-referenced with a data source (e.g., MITRE ATT&K™) to identify one or more attack tactics that a respective asset is vulnerable to. An AAG is generated (804). For example, an AAG generation service (e.g., executed by the AgiHack module of FIG. 6) processes the data representative of the enterprise network to generate an AAG with respect to one or more target assets (crown jewels), the AAG representing one or more paths to each target asset within the enterprise network. In some examples, the AAG is generated as described in U.S. application Ser. No. 16/924,483, introduced above.

A security rules distribution is determined (806). For example, each rule (attack tactic) depicted in the AAG is mapped to one or more SCs (i.e., an SC that mitigates the rule). In some examples, and as described herein, a traceability matrix (TM) is provided, which defines a mapping between SCs and attack tactics (rules). In some examples, a SC can mitigate one or more rules. Accordingly, a rules distribution for each SC can be provided, each rules distribution indicating one or more rules that a respective SC mitigates. A SC influence histogram and a rules distribution are displayed (808). For example, and as described in detail herein, for each SC, an influence score is calculated (e.g., as described herein with reference to Eq. 3), which represents a degree of influence the respective SC has on cyber risk in the enterprise network (e.g., if the SC were to be implemented, how much influence the SC would have in mitigating overall cyber risk). An influence histogram with rules distribution is provided, such as that depicted in FIG. 10A.

Optionally (as indicated in dashed line), a decay method and value are adjusted (810). In some examples, a decay method and value can be preset (e.g., default settings of a simulator). In some examples, the decay method and value can be automatically selected. For example, the influence histogram can be analyzed to determine a type of curve that is represented (e.g., exponential drop, monotonic reduction). In some examples, if the influence histogram is of a first type (e.g., exponential drop), then a first decay method (reduction) (e.g., gradient reduction) is selected. In some examples, if the influence histogram is of a second type (e.g., monotonic reduction), then a second decay method (reduction) (e.g., AUC) is selected. In some examples, the decay method and value are displayed by the simulator, and a user can adjust, if desired.

A reduction is applied (812). For example, and as described herein, the simulator applies the decay method to the AAG based on the value to reduce rules in the AAG, as represented in a resulting residual AAG. In some examples, the decay method is applied until the value is achieved. For example, the value represents a threshold that indicates ending of the decay method for an iteration of simulation (e.g., threshold slope angle, threshold AUC reduction). Prioritized rules and requirements are appended (814). For example, and as described herein, a residual AAG is provided and includes remaining rules as respective SCs. It is determined whether all remaining SCs are mandatory (816). If all remaining SCs are mandatory, a GRV summary is provided (818) and the simulation ends. If not all remaining SCs are mandatory, the example process 800 loops back to execute a next iteration of the simulation.

Implementations of the present disclosure were evaluated through execution of an experiment. The experiment was conducted on virtual network of four active servers. One of the servers had Internet access as a starting point for an attacker. Each server had a Microsoft Windows workstation connected to a Microsoft Active Directory. In the experiments, the environment (enterprise network) was contaminated with a set of vulnerabilities that can be exploited by MITRE ATT&K™ tactics for Active Directory environments. The attack target was defined as the domain controller (DC) server denoted as target X herein. FIGS. 9A-9C depict an evolution of an example AAG over multiple iterations of the experiment. FIGS. 10A-10C depicts an evolution of an influence histogram corresponding to the example AAGs of FIGS. 9A-9C. The experiment included a simulation employing two iterations. The first iteration employed the AUC reduction method, and the second iteration employed the Gradient reduction method. The sequence of reduction techniques was chosen according to the shape of the influence histograms.

The overall reduction results achieved in the experiment are depicted in FIGS. 9A-9C and 10A-10C. In the experiment, the notations of SC₁, SC₂, . . . , SC₁₅ are used to identify different SCs. A mapping is provided that maps attack tactics to corresponding SCs. The purpose of the depicted reduction steps is to minimize the number of possible pathways a hacker can traverse through a computer network, with the goal of ideally eliminating all paths to the DC server (i.e., target, crown jewel).

With particular reference to FIGS. 9A and 10A, an original state is provided and an AAG 900 is generated. The AAG 900 of FIG. 9A represents the original estimation of the SC gap. In the depicted example, the AAG 900 is a 3-dimensional representation of the enterprise network in terms of nodes and edges between nodes. Shades and colors are used for discerning types of a nodes (e.g., medium shade, spherical nodes represent facts, light shade, pyramid nodes represent rules, dark shade, cubical nodes represent impacts). The AAG 900 of FIG. 9A includes 268 attack nodes, of which 159 are rule nodes representing SCRs, 324 edges, and an overall GRV of 6.108. The influence histogram 1000 of FIG. 10A represents the starting condition, which includes 15 SCs that need improvement or are missing. The order of SCs from left to right indicates the prioritization of which SC impacts the cyber posture more and should be handled first.

With particular reference to FIGS. 9B and 10B, a first state is represented after execution of a first iteration. An influence histogram 1002 of FIG. 10B represents the result of applying the first reduction method of AUC with a configuration parameter of 0.4 (indicating 40% area selection). Accordingly, based on the measured data, three SCs with the highest distribution, enumerated as SC₁₅, SC₆, SC₁₀, are removed along with two additional SCs, namely SC₁, SC₁₄. This results in the removal of respective rule nodes from the AAG 900 of FIG. 9A to provide an AAG 902 (residual AAG) of FIG. 9B. The AAG 902 in hand with the influence histogram 1002 indicate that 10 SCs remain after the first iteration. The AAG 902 is much smaller than the AAG 900, now including 146 nodes, of which 60 are rule nodes representing SCRs, 168 edges, and a GRV of 1.624. As a result, a decay ratio of 73% in GRV and 62% decay ratio of SCRs were achieved.

In the second iteration, the Gradient reduction method was applied with gradient value of 0.61, which eliminated SC₂ and SC₇. Since SCs SC₉, SC₃, SC₄, SC₈ include the same rules as SC₂ and SC₇, they were also removed from the inherited AAG containing four residual SCs. This results in the removal of respective rule nodes from the AAG 902 of FIG. 9B to provide an AAG 904 (residual AAG) of FIG. 9C. The AAG 904 is smaller than the AAG 902 and includes 90 nodes, of which 34 are rule nodes representing SCRs, 95 edges, and an overall GRV of 1.02. As a result, an overall a decay ratio of 37% in GRV, and 43% decay ratio of SCRs, were achieved.

In this example, the remaining four SCs include mandatory SCs, namely SCs that cannot be addresses either due to limitations of real systems, or lack of existing SCs at all, indicating a need for future investment. As such, the simulator highlights the order of SCs to be optimized due to lack of tuned implementation, and ones that are needed to be implemented in the future.

In the simulation of the experiment, automatic reduction methods were employed. It can be noted that other selectin criteria can be used, such as Top K and customized selection. The Gradient, AUC, and Top K methods are targeted to remove the most impacting SCs and the custom selection method is aimed at performing manual adjustments.

FIG. 11 depicts a graph 1100 representing the decrease of GRV over the simulation for the example experiment. The graph 1100 illustrates how AAG residual risk is decayed over time, and the level of hackability is reduced once the proposed SCs are implemented. As such, several different decaying method combinations can be explored, in order to find the best decaying curve amongst various decaying methods.

In accordance with implementations of the present disclosure, sub-sets of security controls can be implemented in the enterprise network based on the results of a simulation. For example, and as described herein, each simulation provides a series of sub-sets of security controls and a resulting profile for decrease in GRV. In some examples, at least partially in response to a profile for decrease in GRV, a series of sub-sets of security controls can be implemented in the enterprise network that is represented by the AAG to mitigate cyber risk in the enterprise network. For example, and with reference to the experiment detailed above, a first sub-set of security controls (e.g., SC₁₅, SC₆, SC₁₀) can be initially implemented in the enterprise network, and a second sub-set of security controls (e.g., SC₂, SC₇) can be subsequently implemented in the enterprise network.

As described herein, the CDT platform of the present disclosure provides an approach to automatically gather SCRs based on current security exposure of an enterprise network by analyzing a unique digital twin at least partially provided as an AAG. Implementations of the present disclosure also provide for simulating the implementation of SCs in view of identified SCRs in order to assess their impact on the overall cyber risk reduction of the attack surface. The digital twin of the present disclosure combines detailed information about network assets such as computers, user accounts, firewall rules, and such, with associated known attack tactics.

Further, implementations of the present disclosure provide a simulator that evaluates a proportion of each SC's contribution to the cyber-attack pathways and provides multiple methods to simulate attack surface reduction through potential implementation of SCs. Accordingly, the simulator enables automatic gathering of SCRs that represent where SCs can be implemented, and enables fast reduction of cyber impact and an ordered prioritization of SCs to optimize, followed by constrained or missing security controls for future implementation. The simulator also provides transparency for decision makers regarding the impact of separate SCs and potential risk decay by selecting the order of SCRs and enabling a “what-if” simulation for evaluating the speed of risk reduction. The simulations may be used as a valuable tool in cyber security existing spending and future budget analysis by proposing what needs to be fixed now with employed SCs, and which SCRs, for which SCs are absent.

Implementations and all of the functional operations described in this specification may be realized in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Implementations may be realized as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a computer readable medium for execution by, or to control the operation of, data processing apparatus. The computer readable medium may be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition of matter effecting a machine-readable propagated signal, or a combination of one or more of them. The term “computing system” encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus may include, in addition to hardware, code that creates an execution environment for the computer program in question (e.g., code) that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them. A propagated signal is an artificially generated signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) that is generated to encode information for transmission to suitable receiver apparatus.

A computer program (also known as a program, software, software application, script, or code) may be written in any appropriate form of programming language, including compiled or interpreted languages, and it may be deployed in any appropriate form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program may be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program may be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

The processes and logic flows described in this specification may be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows may also be performed by, and apparatus may also be implemented as, special purpose logic circuitry (e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit)).

Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any appropriate kind of digital computer. Generally, a processor will receive instructions and data from a read only memory or a random access memory or both. Elements of a computer can include a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data (e.g., magnetic, magneto optical disks, or optical disks). However, a computer need not have such devices. Moreover, a computer may be embedded in another device (e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio player, a Global Positioning System (GPS) receiver). Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices (e.g., EPROM, EEPROM, and flash memory devices); magnetic disks (e.g., internal hard disks or removable disks); magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory may be supplemented by, or incorporated in, special purpose logic circuitry.

To provide for interaction with a user, implementations may be realized on a computer having a display device (e.g., a CRT (cathode ray tube), LCD (liquid crystal display), LED (light-emitting diode) monitor, for displaying information to the user and a keyboard and a pointing device (e.g., a mouse or a trackball), by which the user may provide input to the computer. Other kinds of devices may be used to provide for interaction with a user as well; for example, feedback provided to the user may be any appropriate form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any appropriate form, including acoustic, speech, or tactile input.

Implementations may be realized in a computing system that includes a back end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front end component (e.g., a client computer having a graphical user interface or a Web browser through which a user may interact with an implementation), or any appropriate combination of one or more such back end, middleware, or front end components. The components of the system may be interconnected by any appropriate form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”) (e.g., the Internet).

The computing system may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.

While this specification contains many specifics, these should not be construed as limitations on the scope of the disclosure or of what may be claimed, but rather as descriptions of features specific to particular implementations. Certain features that are described in this specification in the context of separate implementations may also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation may also be implemented in multiple implementations separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination may in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.

Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems may generally be integrated together in a single software product or packaged into multiple software products.

A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. For example, various forms of the flows shown above may be used, with steps re-ordered, added, or removed. Accordingly, other implementations are within the scope of the following claims. 

What is claimed is:
 1. A computer-implemented method for mitigating cyber security risk of an enterprise network, the computer-implemented method comprising: receiving an analytical attack graph (AAG) representing paths within the enterprise network with respect to at least one target asset, the AAG at least partially defining a digital twin of the enterprise network and comprising a set of rule nodes, each rule node representing an attack tactic that can be used to move along a path; determining a set of security controls, each security control mitigating at least one rule node in at least a sub-set of rule nodes of the set of rule nodes; executing a first iteration of a simulation representing implementation of a first sub-set of security controls in the enterprise network, the first iteration comprising: for each security control in the set of security controls, determining, a first influence score that represents a change in a security risk that would result from implementing the security control and a rule distribution representing one or more rules that the security control mitigates, defining the first sub-set of security controls based on the first influence scores, and reducing the AAG based on the first sub-set of security controls and a first reduction method to provide a first residual AAG; determining a decrease in a graph risk value based on the AAG and the first residual AAG; and selectively implementing the first sub-set of security controls in the enterprise network at least partially in response to the decrease in the graph risk value.
 2. The computer-implemented method of claim 1, wherein the first reduction method comprises one of a gradient reduction, an area under curve (AUC) reduction, a top k reduction, and a custom reduction.
 3. The computer-implemented method of claim 1, further comprising: executing a second iteration of the simulation representing implementation of a second sub-set of security controls in the enterprise network, the second iteration comprising: for each security control in a residual set of security controls, determining, a second influence score that represents a change in a security risk that would result from implementing the security control and a rule distribution representing one or more rules that the security control mitigates, defining the second sub-set of security controls based on the second influence scores, and reducing the AAG based on the second sub-set of security controls and a second reduction method to provide a second residual AAG.
 4. The computer-implemented method of claim 3, wherein the second reduction method comprises one of a gradient reduction, an area under curve (AUC) reduction, a top k reduction, and a custom reduction.
 5. The computer-implemented method of claim 3, wherein determining a decrease in a graph risk value is further based on the second residual AAG.
 6. The computer-implemented method of claim 3, wherein the residual set of security controls is provided based on a residual set of rule nodes of the first residual AAG.
 7. The computer-implemented method of claim 1, wherein determining a set of security controls at least partially comprises cross-referencing each rule represented in the AAG with a traceability matrix that maps security controls to rules.
 8. The computer-implemented method of claim 1, wherein the first reduction method is automatically selected based on a curve representative of an influence score histogram for the set of security controls.
 9. A system comprising: one or more computers; and one or more storage devices storing instructions that are operable, when executed by the one or more computers, to cause the one or more computers to perform operations for mitigating cyber security risk of an enterprise network, the operations comprising: receiving an analytical attack graph (AAG) representing paths within the enterprise network with respect to at least one target asset, the AAG at least partially defining a digital twin of the enterprise network and comprising a set of rule nodes, each rule node representing an attack tactic that can be used to move along a path; determining a set of security controls, each security control mitigating at least one rule node in at least a sub-set of rule nodes of the set of rule nodes; executing a first iteration of a simulation representing implementation of a first sub-set of security controls in the enterprise network, the first iteration comprising: for each security control in the set of security controls, determining, a first influence score that represents a change in a security risk that would result from implementing the security control and a rule distribution representing one or more rules that the security control mitigates, defining the first sub-set of security controls based on the first influence scores, and reducing the AAG based on the first sub-set of security controls and a first reduction method to provide a first residual AAG; determining a decrease in a graph risk value based on the AAG and the first residual AAG; and selectively implementing the first sub-set of security controls in the enterprise network at least partially in response to the decrease in the graph risk value.
 10. The system of claim 9, wherein the first reduction method comprises one of a gradient reduction, an area under curve (AUC) reduction, a top k reduction, and a custom reduction.
 11. The system of claim 9, wherein operations further comprise: executing a second iteration of the simulation representing implementation of a second sub-set of security controls in the enterprise network, the second iteration comprising: for each security control in a residual set of security controls, determining, a second influence score that represents a change in a security risk that would result from implementing the security control and a rule distribution representing one or more rules that the security control mitigates, defining the second sub-set of security controls based on the second influence scores, and reducing the AAG based on the second sub-set of security controls and a second reduction method to provide a second residual AAG.
 12. The system of claim 11, wherein the second reduction method comprises one of a gradient reduction, an area under curve (AUC) reduction, a top k reduction, and a custom reduction.
 13. The system of claim 11, wherein determining a decrease in a graph risk value is further based on the second residual AAG.
 14. The system of claim 11, wherein the residual set of security controls is provided based on a residual set of rule nodes of the first residual AAG.
 15. The system of claim 9, wherein determining a set of security controls at least partially comprises cross-referencing each rule represented in the AAG with a traceability matrix that maps security controls to rules.
 16. The system of claim 9, wherein the first reduction method is automatically selected based on a curve representative of an influence score histogram for the set of security controls.
 17. A non-transitory computer-readable medium storing software comprising instructions executable by one or more computers which, upon such execution, cause the one or more computers to perform operations for mitigating cyber security risk of an enterprise network, the operations comprising: receiving an analytical attack graph (AAG) representing paths within the enterprise network with respect to at least one target asset, the AAG at least partially defining a digital twin of the enterprise network and comprising a set of rule nodes, each rule node representing an attack tactic that can be used to move along a path; determining a set of security controls, each security control mitigating at least one rule node in at least a sub-set of rule nodes of the set of rule nodes; executing a first iteration of a simulation representing implementation of a first sub-set of security controls in the enterprise network, the first iteration comprising: for each security control in the set of security controls, determining, a first influence score that represents a change in a security risk that would result from implementing the security control and a rule distribution representing one or more rules that the security control mitigates, defining the first sub-set of security controls based on the first influence scores, and reducing the AAG based on the first sub-set of security controls and a first reduction method to provide a first residual AAG; determining a decrease in a graph risk value based on the AAG and the first residual AAG; and selectively implementing the first sub-set of security controls in the enterprise network at least partially in response to the decrease in the graph risk value.
 18. The non-transitory computer-readable medium of claim 17, wherein the first reduction method comprises one of a gradient reduction, an area under curve (AUC) reduction, a top k reduction, and a custom reduction.
 19. The non-transitory computer-readable medium of claim 17, wherein operations further comprise: executing a second iteration of the simulation representing implementation of a second sub-set of security controls in the enterprise network, the second iteration comprising: for each security control in a residual set of security controls, determining, a second influence score that represents a change in a security risk that would result from implementing the security control and a rule distribution representing one or more rules that the security control mitigates, defining the second sub-set of security controls based on the second influence scores, and reducing the AAG based on the second sub-set of security controls and a second reduction method to provide a second residual AAG.
 20. The non-transitory computer-readable medium of claim 19, wherein the second reduction method comprises one of a gradient reduction, an area under curve (AUC) reduction, a top k reduction, and a custom reduction.
 21. The non-transitory computer-readable medium of claim 19, wherein determining a decrease in a graph risk value is further based on the second residual AAG.
 22. The non-transitory computer-readable medium of claim 19, wherein the residual set of security controls is provided based on a residual set of rule nodes of the first residual AAG.
 23. The non-transitory computer-readable medium of claim 17, wherein determining a set of security controls at least partially comprises cross-referencing each rule represented in the AAG with a traceability matrix that maps security controls to rules.
 24. The non-transitory computer-readable medium of claim 17, wherein the first reduction method is automatically selected based on a curve representative of an influence score histogram for the set of security controls. 